Problem: Find the integer $n,$ $0 \le n \le 180,$ such that $\cos n^\circ = \cos 758^\circ.$
Explanation: Since the cosine function has period $360^\circ,$
\[\cos 758^\circ = \cos (758^\circ - 2 \cdot 360^\circ) = \cos 38^\circ,\]so $n = \boxed{38}.$